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arXiv · 1910.12364

Neighbor connectivity of $k$-ary $n$-cubes

Tomáš Dvořák·Mei-Mei Gu
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Abstract

The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an interconnection network, this means that the failure of a network node causes failures of all its neighbors. We completely determine the neighbor connectivity of $k$-ary $n$-cubes for all $n\ge1$ and $k\ge2$.

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Tomáš Dvořák, Mei-Mei Gu. 2019-10-27. Neighbor connectivity of $k$-ary $n$-cubes. https://arxiv.org/abs/1910.12364

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